Tests, Power and Significance

In the mathematical statistics course today, we started talking about tests, and decision rules. To illustrate all the concepts introduced today, we considered the case where we have a sample with . And we want to test

against

In the course, we’ve seen that we could use a test based on the order statistics . The test would be

Why not consider a test based on ? The problem is that we need the distribution (more specifically the survival distribution) of . We can compute it, numerically. But that might be painful. An alternative is to consider some approximation, based on the central limit theorem, i.e.

Our test is based on , and to get the same significance as before, use

An Open Lab-Notebook Experiment

Some
sort of unpretentious (academic) blog, by a surreptitious economist and
born-again mathematician. A blog activist, and an actuary, too. Always curious.
Because academics are probably more than the sum of our publication lists, grants and conference talks...

Used to live in Paris (France),
Leuven (Belgium), Hong-Kong (China), and Montréal (Canada). Professor and researcher in
Montréal, currently back in Rennes (France). ENSAE ParisTech & KU Leuven Alumni